IV. ESTIMATES BASED ON ONE CENSUS ONLY

1. Importance of a census for accurate population which are discussed elsewhere in this Manual. The use estimates of birth death and migration statistics for this purpose is considered in chapter VI,2 and the assumption,of a plausible rate of increase, where no better method :an A census is defined for the present purpose as an be found, is taken up in chapter II.l The followmg individual enumeration of the whole population, or at paragraphs refer to two methods which are particularly least a great majority of the population, during a period likely to be useful in a country where a census has been of not more than one year. Though censuses vary taken for the first time: (a) the calculation of rates of greatly in accuracy, as a rule they give much more increase from results of non-censal counts, and (b) the reliable measures of population size than non-censal estimation of rates of increase from data obtained in determina~ counts. The main reason for this is that the the census itself. tion of population size is one of the primary objectives of a census; the census procedure is designed to realize If non-censal counts were used to estimate the popu­ this objective as accurately as possible. lation before the census was taken, these may permit an estimate of the increase after the census date. The first census taken ina country is usually not as Example. In the census of Tanganyika as of 2 August 1948, accurate as subsequent censuses can be, since successful a population of 7,477,677 was returned. There was no reason census-taking under the conditions prevailing in any to suppose that this figure was too high or too low. Comparison country is in part a matter of local experience. It is of the census total with previous estimates based largely on highly important for purposes of population estimates tax lists and group enumerations showed that the latter were to evaluate the accuracy of a census enumeration and too low. The estimate for 1947 was 5,838,000 and that for to "correct" the census result accordingly if it is found 1928 was 4,741,000. O'n the assumption that the extent of under­ estimation was the same in 1947 as in 1928, the average annual that there have been omissions or double counting. The increase during the interval was calculated at 1.1 per cent. accuracy of a first census is, however, more difficult to One method of estimating the mid-year 1949 population (though appraise than that of subsequent enumerations, which not the one used in making the official estimate) is to add provide the means of a comparison of results for two eleven-twelfths of 1.1 per cent to the 1948 census total, which gives an estimate of 7,550,000, (The fraction, eleven-twelfths, or more dates. is used because the 1948 census date was one month after the The accuracy of population estimates based on a middle of the year.) census is, of course, greatly affected by the length: of The derivation of an assumed rate of increase from the time interval which has elapsed since that census non-censal counts rests on an assumption that the non­ was taken. We shall, therefore, give separate considera­ censal counts for various years have erred in the same tion to estimates based on a recent census and to those direction and to the same extent. This assumption may based on a census taken in a more distant past, assum­ not be tenable in some cases. Non-censal counts per­ ing in both cases that this was the country's only censu!>. formed after the taking of the census may differ in accuracy from those performed before the census, 2. Estimates based on one recent census particularly if the staff employed for the non-censal counts take advantage of the information and experi­ For the date of the census, the census result can be ence acquired at the census. If counts of unequal regarded as the best possible estimate of population accuracy are compared, the derivation of an estimated size, provided there is no reason to believe that it is rate of increase is still possible by arbitrarily selecting above or below the mark. If there is evidence of over~ a value somewhere between extreme values resulting enumeration or under-enumeration, the census figure from the comparison of several counts. should be "corrected" and it should be stated, in the It is usually not safe to derive a rate of increase publication giving the subsequent estimates of popula­ directly from a comparison of a non-censal count with tion, that this correction has been made. the census result, as the latter is probably more accurate Time adjustment for population changes since the and not subject to the same kinds of error. census date! can be made in a number of ways, some of Given some knowledge of the mortality rates, the •A ume adjustment is needed even in making an estimate for rate of population increase may sometimes be estimated, the year of the census, unless the census was taken near the middle of the year. The census result should be increased or • Comprehensive data on these subj ects are likely not to be diminished by the estimated amount of population change during available in countries where the first census has recently been the fraction of the year between the census date and 1 July, taken. in order to ensure comparability with other mid-year estimates. • See chapter II, section 6. 25 at least very rougWy, from the results of the census of the enumerated population. The resulting informa­ itself, classified by age groups. A possible way of esti­ tion made it possible to estimate rates of births, deaths mating the birth rate is to use the number of infants and natural increase prevailing in these territories. aged under one year who w~re enumerated at the census, These estimated rates are being used in making esti­ with suitable allowance for infant mortality, to arrive at mates of current population size. Fertility and mortality the number of births in the preceding year from which rates can be estimated also by means of sampling these infants have survived. The method, of course, re­ investigations independent of the census. This is being quires some information about infant mortality. More­ done at present in a selected area of India, in the course over, few censuses succeed in an accurate enumeration of of a field study being conducted jointly by the United infants. Considerable proportions of infants under one Nations and the Indian Government. The experience year of age are often omitted from the enumeration, obtained in that study is expected to be helpful as a while some of those enumerated may be reported as guide for similar investigations in other countries where more than one year old. A comparison of the numbers reliable vital statistics are lacking. of infants reported as under one year of age with the numbers reported at ages of one, two, three, or four 3. Estimates based on a census taken in the more years may provide some basis for correcting the figure distant past for the age under one year, and thus lead to an im­ proved estimate of the birth rate. By similar methods, The usefulness of a census result for current popula­ estimates of births over a period of several years may tion estimates diminishes with the passage of time, for be made from the returns on children of various ages. two reasons. On the one hand, cumulative errors due Example. Mortara, utilizing the results of the Brazilian to inaccurate assumptions with respect to population census of 1920, estimated the birth rate of Brazil during the growth tend to remove current population estimates more years 1910-20 on the assumption of certain coefficients of survival and more from reality the more time has elapsed since the and inaccuracies in age statements. last census. On the other hand, in most countries where That ages were reported inaccurately could be seen from the there has been a census at some time in the past, other fact that more children were reported at ages of 2 or 3 years statistical series have also been established and their than at ages of one or under one year. However, despite this inaccuracy, Mortara applied survival coefficients to these accuracy has been improved. Eventually reliance on numbers to arrive at a first approximation, as follows: other statistical information leads to better estimates Number of than reference to an old census. Years Persons Coefficient births Year Example. A census has been taken, the result of which is of enumer­ of (first preceding believed to have been in error by no more than 3 per cent. The age ated survival estimate) cet/-SUs error in annual estimates of population increase may be, on the 1 828,000 0.883 934,000 1 average, 0.5 per cent of the population. The cumulative effect 2 776,000 0.780 996,000 2 of the .latter error can lead, after twenty years, to a total error 3 1,015,000 0.736 1,378,000 3 in estimates amounting to 3 per cent plus 20 times 0.5, i.e., to 4 1,006.000 0.717 1,404,000 4 13 per cent of the population. 5 950,000 0.706 1,345,000 5 Supposing also that non-censal counts, which are taken 6-10 4,537,000 6,576,000 6-10 regularly, can be used to make population estimates subject to an error of no more than 10 per cent. It appears that, after TOTAL 9,112,000 12,636,000 twenty years, it is better to rely on the non-censal counts for Assuming that a total of about 12,500,000 births had indeed current estimates than to continue basing them on the census result. occurred during the ten years preceding the census, but allow­ ing for the fact that,· in an increasing population, the annual This does not mean that the census loses all its useful­ number of births increases under a fairly constant birth rate, ness, because it can still be utilized in an appraisal and he recomputed the series with corrected estimates. According to improvement of current statistics. A census, even these second estimates, the number of births in the year though taken in the remote past, may also be very preceding the census was about 1,363,000, and the estimated birth rate was 47.2 per 1,000.' helpful in the design of samples for current investiga­ tions of the population.s Census data on population by age groups can be used In some countries, no national census has been taken also to estimate the death rate, but in this case the for a long time, but there have been provincial censuses results of at least two censuses are ordinarily needed from time to time. A comparison of the results of such for accurate estimation. provincial censuses with those of the previous national Information regarding fertility and mortality can census may be used for estimating the increase in the alga be obtained from special questions asked in a population of the country as a whole since the date of census enumeration, eit1).er of the whole population or the national census, with appropriate allowance for a sample. On the occasion of the censuses of Tangan­ differences in the rates of increase in various parts of yika, Kenya and Uganda, in 1948, questions relating the country. to the numbers of births and deaths which had occurred In Argentina, for instance, no national census was in the preceding year were asked among 10 per cent taken during the interval from 1914 to 1947. However, • United Nations. Methods of using census statistics for the censuses were taken in the cities of Buenos Aires calculation of life tables and other demographic measures (1936) and Santa Fe (1923), in the provinces of (with application to the population of Brazil). By Giorgio Mortara. Lake Success, November 1949, pp. 14-16. • See appendix B.

26 Buenos Aires (1938) and Mendoza (1942), in Chaco line with actual population changes..Hence a great Territory (1934), Pampa Territory (1935), and Na­ interest attaches to the availability of vital statistics, by tional Territories (1920). Censuses of children of means of which the value of the census results can be school age were taken in Santa Fe province (1912, preserved over a longer period of time. Sampling for 1918, 1925, and 1937) and in Rosario city (1934).6 estimates of birth and death rates can be very helpful The results of these local censuses, together with the where it is not found practicable to establish a well­ current registration statistics of births, deaths and functioning registration system within any short time. migration, probably permitted fairly adequate provin­ Sampling, however, is at best a poor substitute for a cial population estimates to be maintained during the complete system of vital registers. long period between the two national population In the absence of statistics of births and deaths, the censuses. considerations whi'ch should govern the assumption of There may be reason to believe that in the period rates of increase, and the kind of information which since the last census the completeness of birth and death may be helpful in making such assumptions, have been registration has improved. If so, current estimates may discussed in preceding chapters and should also apply eventually have to be reconstructed: earlier estimates where a census has been taken. However, as was in post-censal years, when birth and death registration shown in the present chapter, special methods for the was presumably less accurate, may have to be revised derivation of possible rates of increase can also be used before an improved series of post-censal estimates can where a census result is available. A combination of be carried up to the current date. all possible information is likely to lead to more realistic assumptions than the reliance on one method only. 4. Evaluation and improvement of the quality of Information on the accuracy of a country's first estimates based on one census only census can best be obtained in quality checks by means Where the results of one census are available, the of samples;7 the census itself also provides various most obvious method of improving current population internal evidence of its possible degree of accuracy; estimates is to taken another census. Owing to the fact discussion of this topic is, however, reserved for a later that the taking of a census involves important con­ manual. siderations of planning and expense, frequent census The appraisal of the quality of non-censal statistics . taking is not always practicable. But after a long time is often possible in the light of the census, particularly the results of a census lose most of their usefulness if non-censal counts were taken near the date of the especially where the registration of births and deaths census. Such knowledge is of importance if the census and the records of migration are not very accurate, or is rather old and if more reliance must be placed on are lacking entirely. Under those conditions, after non-censal data for purposes of current estimates. twenty years or so, the state of information about the For all estimates based on a census, care should be population is little better than if no census had ever taken that the definition of the population (de jure, been taken. If it is intended to maintain a standard of de facto, etc.) corresponds if possible to international statistical information above that of countries in which standards. If necessary, census figures may be adjusted there has been no census, the census must be repeated. by means of estimated numbers of persons in certain As an alternative, though not an entirely adequate categories, in order to conform to the standard defini­ substitute, a sample census may be taken. Even after tion of the total population. The definition of the a considerable number of years has passed, the results population, if deviating from international standards, of a previous census can provide a framework for a should be indicated. highly efficient sample census, an opportunity which Some censuses, although conducted in the greater should always be kept in mind. part of the country, or for a majority of its population, The rapidity with which" the results of a previous do not include special parts of the population (e.g., census lose their usefufness depends on the accuracy tribal Indians, displaced persons, merchant seamen of information with regard to rates of population aboard vessels, etc.). To obtain estimates of total popu­ change. If only vague assumptions regarding rates of lation, special estimates must be made for these cate­ increase can be made, errors of estimates accumulate gories and added to the census total, with indication very rapidly. If, on the other hand, tolerably accurate that this was done. I f the numbers involved in the vital statistics are at hand, a longer interval of time. adjustment are large, it is desirable that they be also may pass before time adjustments fall greatly out of shown separately with statement of the method by \",ruch they were estimated. • United States Bureau of the Census. Argentina. Summary of Biostatistics. Washington, February 1945, pp. 7-9. • See appendix B.

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